Bias-corrected maximum likelihood estimators of the parameters of the inverse Weibull distribution

ABSTRACT

Maximum likelihood estimators usually have biases of the order $\mathcal{O}\left(n^{-1}\right)$ for large sample size n which are very often ignored because of the fact that they are small when compared to the standard errors of the parameter estimators that are of order $\mathcal{O}\left(n^{-1/2}\right)$. The accuracy of the estimates may be affected by such bias. To reduce such bias of the MLEs from order $\mathcal{O}\left(n^{-1}\right)$ to order $\mathcal{O}\left(n^{-2}\right)$, we adopt some bias-corrected techniques. In this paper, we adopt two approaches to derive first-order bias corrections for the the maximum likelihood estimators of the parameters of the Inverse Weibull distribution. The first one is the analytical methodology suggested by Cox and Snell (1968) and the second is based on the parametric Bootstrap resampling method. Monte Carlo simulations are conducted to investigate the performance of these methodologies. Our results reveal that the bias corrections improve the accuracy as well as the consistency of the estimators. Finally, an example with a real data set is presented.

KEYWORDS:

• Bootstrap bias-correction
• Cox-Snell bias-correction
• Inverse Weibull distribution
• Maximum likelihood estimators
• Monte Carlo simulation

Mathematics Subject Classification:

• 62F10
• 62F40
• 62N02
• 62N05

Acknowledgments

The authors would like to thank the Editor-in-Chief, Associate Editor and the referee for careful reading and for comments which greatly improved the paper.